Event
Subset of the set of possible outcomes of a random experiment.
An event can include one or more possible outcomes.
Notation
As the subset of a set, an event can be noted extensionally or intentionally.
In the case of a random experiment that consists of rolling an honest die with 6 faces numbered 1 to 6, the event "getting an even number" has three possible results: {2, 4, 6}.
- E = {x ∈ Ω | x is even} (intensional definition of a set)
- E = {2, 4, 6} (extensional definition of a set).
- E: "getting an even number",
- E: getting an even number.
Examples
- In the random experiment that consists of rolling an honest die with 6 faces numbered 1 to 6, the event that consists of getting a number less than 3 includes two possible results: {1, 2}.
- In the random experiment that consists of drawing a ball from a bag that contains red, blue, and yellow balls, the event that consists of drawing a ball that is not red includes 2 possible results: {blue, yellow}.
- In the random experiment that consists of rolling an honest die with six faces numbered 1 to 6 and recording the result that appears on the top face, the subset formed by the results 2, 4 and 6, or {2, 4, 6}, forms the event "getting an even number".